Numerous applications such as on-line banking, on-line commerce, etc. involve sending sensitive information over a network. Some form of cryptography is typically employed in order to enhance the security of the sensitive information as it traverses the network. One type of encryption, referred to as keyed encryption, passes a key to the receiver of sensitive information. The key helps reverse the cryptography process such that an encoded or encrypted message is correctly decoded.
In many keyed encryption applications, the sensitive message is scrambled with random data. For example, the Vernam cypher method uses a random numeric key (i.e., a stream or sequence of random numbers) that is added to a stream of sensitive data to generate encrypted data. If the numbers of the key are truly random it is theoretically impossible to decode the encrypted data without the key. Thus, generally, as random number generators become less pseudo-random and more truly random, the probability that a "hacker" will be able to break the code (i.e., produce the random sequence) declines.
As such, a figure of merit of keyed encryption technology focuses on the randomness of the key sequence (also referred to as a "sequence")--with perfect randomness being the ultimate desired goal of the signal used to generate the sequence. A perfectly random signal is typically referred to as theoretically perfect "white noise". FIG. 1a, shows the magnitude of theoretically perfect white noise 100 in the frequency spectrum. Theoretically perfect white noise 100 is primarily characterized by two features: 1) infinite bandwidth 101; and 2) identical noise power amplitude 102 across all frequencies.
Although theoretically perfect white noise is difficult or perhaps impossible to achieve, signals that begin to approach the characteristics shown in FIG. 1a may be referred to as white noise. Thus white noise refers to signals that, although less then theoretically perfect, still resemble such a signal. Indicia include an approximately even amplitude across a wide bandwidth. The inverse Fourier transform of white noise is a random signal 201 such as that seen in FIG. 2. By definition, a perfectly random stream will flip up 50% of the time and flip down 50% of the time.
Random number generators are typically designed to sample a white noise signal 201 at a plurality of successive sample times 202a,b,c,d,e. Each successive sample time corresponds to a new value 203a,b,c,d,e in the random sequence 204. Generally, flips up 205a,b,c are "1s" 203a,b,c while flips down 206a,b are "0s" 203c,e. That is, the white noise is typically fed to a zero cross detector, threshold detector or other decision device.
As the channel bandwidth falls short of infinity the noise spikes seen in the random signal 201, widen. This results in less noise spike flips between sampling times as compared to perfect white noise. If fewer noise spike flips occur between sampling times, the sampled value may be viewed as being more dependent on the previous sample value. Better said, as the number of flips occurring between sampling times approach infinity, the probability that 50% are up and 50% are down approaches 1.00. Thus wider noise spikes correspond to less than perfect randomness.
Furthermore, as shown in FIG. 1b, any periodic activity associated with the channel that processes the white noise may introduce strong signal power 106 at the frequency 107 (or multiple thereof) of the periodic activity. These features are generally referred to as harmonics or tones. The presence of harmonics diminish the randomness of the sequence. That is, the sequence may have a predictable pattern of 1s or 0s corresponding to the frequency of the tone.
Therefore, channels designed to process white noise for use in random number generators should emphasize high bandwidth as well as the suppression of tones (regardless of tone source). Such a design is difficult to achieve in practice with semiconductor amplifiers. Many amplifiers posses 1/f noise which increases the noise voltage at low frequencies. This may be viewed as the presence of a continuous spectrum of tones, in the lower frequency portion of the channel. Furthermore, amplifiers having high enough gain bandwidth product to successfully amplify noise to a level where a decision device can make a decision yet still have enough bandwidth to introduce enough flips between sampling times are difficult to design. Also, amplifiers possess voltage offsets that bias the noise signal resulting in decision rates other than 50% 1 and 50% 0.